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Transient rotational flow of an Oldroyd-\(B\) fluid over a disk. (English) Zbl 0827.76006
The transient flow of an Oldroyd-B fluid over an infinite disk set in rotation impulsively is studied under the similarity assumptions. The unsteady velocity and stress field are calculated exactly for short times by a power series expansion in time. The order of magnitude of the velocity and stress components is found to depend on the relative magnitude of the Deborah number and the ratio of solvent to polymeric viscosities. When either one becomes very small, a solution using singular perturbations and Laplace transforms is developed. Numerical calculations are used to determine the extent of validity of the present results.

MSC:
76A10 Viscoelastic fluids
76U05 General theory of rotating fluids
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